COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Complex Analysis * MT   433 7 3 3 5

Prerequisites and co-requisites
Recommended Optional Programme Components None

Language of Instruction Turkish
Course Level First Cycle Programmes (Bachelor's Degree)
Course Type
Course Coordinator Assoc.Prof.Dr. Nazar Şahin ÖĞÜŞLÜ
Instructors
Doç.Dr.NAZAR ŞAHİN ÖĞÜŞLÜ1. Öğretim Grup:A
Doç.Dr.NAZAR ŞAHİN ÖĞÜŞLÜ2. Öğretim Grup:A
 
Assistants
Goals
Calculate certain integrals of some special types of complex functions, write and prove that the sum of series formulas, find the sum of the series, explain the relationship between zeros and poles of a complex function in an area, find the number of zeros and poles of a complex function in an area, decide whether a function conformal and can apply on curves, explain the relationship between the convergence of an infinite multiplication with convergence of an infinite series, calculate some of the infinite multiplication.
Content
Integrals, sum of series, poles and zeros, conformal mappings, infinite multiplication

Learning Outcomes
-


Course's Contribution To Program
NoProgram Learning OutcomesContribution
12345
1
Is able to prove Mathematical facts encountered in secondary school.
X
2
Recognizes the importance of basic notions in Algebra, Analysis and Topology
X
3
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
X
4
Is able to express basic theories of mathematics properly and correctly both written and verbally
X
5
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
X
6
Expresses clearly the relationship between objects while constructing a model
X
7
Draws mathematical models such as formulas, graphs and tables and explains them
X
8
Is able to mathematically reorganize, analyze and model problems encountered.
X
9
Knows at least one computer programming language
X
10
Uses effective scientific methods and appropriate technologies to solve problems
X
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
X
12
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields
X
13
Knows programming techniques and is able to write a computer program
X
14
Is able to do mathematics both individually and in a group.
X

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
1 General information, derivative, Cauchy-Riemann equations, analytic functions, Cauchy-Gaursat theorem, series and residual calculations, brief review. Review of the relevant pages from sources
2 Integrals Review of the relevant pages from sources
3 Calculation of definite integrals contaning sine and cosine expressions. Review of the relevant pages from sources
4 Definite integrals of multi-valued functions. Review of the relevant pages from sources
5 Cauchy principal value and trigonometric integrals. Review of the relevant pages from sources
6 Proof of formulas of the sum of series. Review of the relevant pages from sources
7 Applications related to the calculation of the sum of series. Review of the relevant pages from sources
8 Written exam topics discussed in the lecture notes and sources again
9 Mittag-Lefflers theorem, proof and applications. Review of the relevant pages from sources
10 Proof of formulas related to the relationship between zeros and poles and its applications. Review of the relevant pages from sources
11 Rouche theorem and its applications. Review of the relevant pages from sources
12 Conformal mappings. Review of the relevant pages from sources
13 Applications related to conformal mappings Review of the relevant pages from sources
14 Definition and properties of infinite products. Review of the relevant pages from sources
15 Some applications related to infinite products. Review of the relevant pages from sources
16-17 Final exam topics discussed in the lecture notes and sources again

Recommended or Required Reading
TextbookCOMPLEX VARIABLES AND APPLICATIONS, Authors: Ruel V. Churchill, James Ward Brown
Additional Resources
KOMPLEKS FONKSİYONLAR TEORİSİ, Yazar: Prof.Dr. Turgut Başkan
KARMAŞIK FONKSİYONLAR KURAMI, Yazar: Prof.Dr. Ali Dönmez